基于最大熵原理的谐波求和问题
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摘要
针对电力系统中具有不同相角分布时随机谐波矢量(电压和电流)求和问题,采用最大熵原理求取谐波矢量和幅值(简称和值)的概率密度分布。通过各随机矢量X、Y正交分解后的统计特征(各阶矩)合成得和值的统计特征,由最大熵原理仅需4阶矩就能很好地逼近矢量和值的概率密度函数PDF(Probability Density Function),进而获得相应的95%概率值,避免了递推高阶矩所带来的误差;且求和时不需要各个随机矢量在相位上具有0～2π的均匀概率分布,适用于小样本情况。最后用实际测量值进行的对比分析验证了该方法的有效性。
This paper presents a new method by using principle of maximum entropy to obtain the probability density distribution of sum of random harmonic vectors(voltage or current) whose phases have different probability distribution functions in a power system.Several vectors are decomposed with X-Y axis.Obtaining the summation of random vectors by that of their high order moments and through the iteration of moments of given vectors' X-Y axis components,the PDF of the sum of vectors is obtained by using principle of maximum entropy and only needing 4-order moments,and then obtaining the probability value of 95% of the sum of vectors,avoiding the error of iteration of calculating the high moments.The kind of summation method does not require the probability distribution of each random vector is within the interval(0,2π) in phase angle,so less statistical samples value is to be used.The analysis on practical measured values and comparison with other method prove that the proposed method is effective.
This paper presents a new method by using principle of maximum entropy to obtain the probability density distribution of sum of random harmonic vectors(voltage or current) whose phases have different probability distribution functions in a power system.Several vectors are decomposed with X-Y axis.Obtaining the summation of random vectors by that of their high order moments and through the iteration of moments of given vectors' X-Y axis components,the PDF of the sum of vectors is obtained by using principle of maximum entropy and only needing 4-order moments,and then obtaining the probability value of 95% of the sum of vectors,avoiding the error of iteration of calculating the high moments.The kind of summation method does not require the probability distribution of each random vector is within the interval(0,2π) in phase angle,so less statistical samples value is to be used.The analysis on practical measured values and comparison with other method prove that the proposed method is effective.
引文
[1]杨洪耕,肖先勇,刘俊勇.电能质量问题的研究和技术进展(二)-供电网谐波的测量与分析[J].电力自动化设备,2003,23(11):1-4.YANG Hong-geng,XIAO Xian-yong,LIU Jun-yong.Issues and Technology Assessment on Power Quality Part2:Measurement and Analysis for Harmonic in Supply Network[J].Electric Power Automatic Equipment,2003,23(11):1-4.
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[10]王栋,朱元牲.最大熵原理在水文水资源科学中的应用[J].水科学进展,2001,12(3):424-430.WANG Dong,ZHU Yuan-sheng.Principle of Maximum Entropy and Its Application in Hydrology and Water Resources[J].Advances in Water Science,2001,12(3):424-430.
[11]朱坚民,郭冰菁,王中宇,等.基于最大熵方法的测量结果估计及测量不确定度评定[J].电测与仪表,2005,42(476):5-8.ZHU Jian-min,GUO Bing-jing,WANG Zhong-yu,et al.Study on Evaluation of Measurement Result and Uncertainty Based on Maximum Entropy Method[J].Electrical Measurement&Instrumentation,2005,42(476):5-8.
[12]刁艳芳,王本德,刘冀.基于最大熵原理方法的洪水预报误差分布研究[J].水利学报,2007,38(5):591-595.DIAO Yan-fang,WANG Ben-de,LIU Ji.Study on Distribution of Flood Forecasting Errors by the Method based on Maximum Entropy[J].Shuili Xuebao,2007,38(5):591-595.
[13]冯利华.最大熵原理与地震频度-震级关系[J].地震地质,2003,25(2):260-264.FENG Li-hua.Maximum Entropy Principle and Seismic Magnitude-frequency Relation[J].Seismology and Geology,2003,25(6):260-264.
[2]Testa A,Langella R.Considerations on Probabilistic Harmonic Voltages[A].In:IEEE Power Engineering Society General Meeting[C].Toronto(Canada):2003.1154-1159.
[3]Abdi A,Homayoun H.On the PDF of Random Vectors[J].IEEE Trans on Communication,2000,48(1):7-11.
[4]Primak S,Vetri J L,Roy J.On the Statistics of a Sum of Harmonic Waveforms[J].IEEE Tran on Electromagnetic Compatibility,2002,44(1):266-270.
[5]Carbone R,Carpinelli G,Morrison R E,et al.A Review of Probabilistic Methods for the Analysis of Low Frequency Power System Harmonic Distortion[A].In:9th IEE International Conference on Electromagnetic Compatibility[C].Manchester(UK):1994.148-155.
[6]Van C J,Groeman F.Harmonic Analysis of Rail Transportation[A].In:Systems with Probabilistic Techniques Probabilistic Methods Applied to Power Systems International Conference[C].2006.
[7]张晶.多谐波源系统谐波叠加方法的研究[J].电网技术,1995,19(3):23-27.ZHANG Jing.Studies of Harmonics Superposition Method in Multi-harmonic Sources System[J].Power System Technology,1995,19(3):23-27.
[8]王磊,杨洪耕.基于Laguerre多项式的谐波求和问题[J].电力系统自动化,2005,29(4):40-44.WANG Lei,YANG Hong-geng.Summation of Random Harmonic Vectors Based on Laguerre Polynomials[J].Automation of Electric Power Systems,2005,29(4):40-44.
[9]杨洪耕,秦东,张正书,等.用Laguerre多项式描述谐波随机求和问题[J].电网技术,2005,29(14):26-29.YANG Hong-geng,QIN Dong,ZHNAG Zheng-shu,et al.A Study on Summation of Harmonic with Random Phases Angles Based on Laguerre Polynomials[J].Power System Technology,2005,29(14):26-29.
[10]王栋,朱元牲.最大熵原理在水文水资源科学中的应用[J].水科学进展,2001,12(3):424-430.WANG Dong,ZHU Yuan-sheng.Principle of Maximum Entropy and Its Application in Hydrology and Water Resources[J].Advances in Water Science,2001,12(3):424-430.
[11]朱坚民,郭冰菁,王中宇,等.基于最大熵方法的测量结果估计及测量不确定度评定[J].电测与仪表,2005,42(476):5-8.ZHU Jian-min,GUO Bing-jing,WANG Zhong-yu,et al.Study on Evaluation of Measurement Result and Uncertainty Based on Maximum Entropy Method[J].Electrical Measurement&Instrumentation,2005,42(476):5-8.
[12]刁艳芳,王本德,刘冀.基于最大熵原理方法的洪水预报误差分布研究[J].水利学报,2007,38(5):591-595.DIAO Yan-fang,WANG Ben-de,LIU Ji.Study on Distribution of Flood Forecasting Errors by the Method based on Maximum Entropy[J].Shuili Xuebao,2007,38(5):591-595.
[13]冯利华.最大熵原理与地震频度-震级关系[J].地震地质,2003,25(2):260-264.FENG Li-hua.Maximum Entropy Principle and Seismic Magnitude-frequency Relation[J].Seismology and Geology,2003,25(6):260-264.
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